Method for manufacturing in-plane lattice constant adjusting substrate and in-plane lattice constant adjusting substrate

ABSTRACT

A method of adjusting the in-plane lattice constant of a substrate and an in-plane lattice constant adjusted substrate are provided. A crystalline substrate ( 1)  made of SrTiO 3  is formed at a first preestablished temperature thereon with a first epitaxial thin film ( 2 ) made of a first material, e. g., BaTiO 3 , and then on the first epitaxial thin film ( 2 ) with a second epitaxial thin film ( 6 ) made of a second material, e. g., BaxSr 1-x TiO 3  (where 0&lt;x&lt;1), that contains a substance of the first material and another substance which together therewith is capable of forming a solid solution in a preestablished component ratio. Thereafter, the substrate is heat-treated at a second preselected temperature. Heat treated at the second preestablished temperature, the substrate has dislocations ( 4 ) introduced therein and the second epitaxial thin film ( 6 ) has its lattice constant relaxed to a value close to the lattice constant of bulk crystal of the second material. Selecting the ratio of components x of the other substance in the second material allows a desired in-plane lattice constant to be realized.

TECHNICAL FIELD

[0001] The present invention relates to a method of preparing anin-plane lattice constant adjusted substrate, and an in-plane latticeconstant adjusted substrate, whereby a desired in-plane lattice constantcan be realized.

BACKGROUND ART

[0002] A thin film formed so that it is epitaxially grown on acrystalline substrate has its properties influenced by its crystallineperfectness. For example, in the preparation of an oxide superconductorthin film such as of (Ba, Sr) CuO type which is epitaxially grown on asubstrate to form a laminated superconductor, its superconductivetransition temperature and superconductive critical magnetic field areinfluenced by its crystalline perfectness such as its crystal defectdensity and crystallographic orientation. Also, an epitaxial BaTiO₃ thinfilm used as a memory element in a semiconductor integrated circuit hasits capacity value largely varied by its crystallographic orientation.

[0003] So far, in order to obtain a high quality thin film that issatisfactory in crystalline perfectness, a substrate has been usedhaving an in-plane lattice constant that is close to the in-planelattice constant of the thin film. If there does not exist any substratehaving an in-plane lattice constant close to that of a thin film, amaterial is chosen having an in-plane lattice constant intermediatebetween those of the substrate and the thin film and is layered on thesubstrate as a buffer layer on which the thin film may be grown.

[0004] It is, however, only rare that a substrate is available thatagrees in in-plane lattice constant with the thin film, and if such asubstrate is available, it often is extremely brittle or of high cost.In the use of a buffer layer, too, it rarely is the case that asubstrate is available which is fully congruous in in-plane latticeconstant.

[0005] Thus, in the past, since it has not been possible to grow a thinfilm on a substrate that fully agrees or is congruent in in-planelattice constant therewith, it has been likely the case that a thin filmhas dislocations introduced therein due to its lattice mismatch with thesubstrate; hence a thin film results that is highly dense with crystaldefects, imperfect in crystalline orientation, and thus poor in qualityand properties, problems met by the prior art.

DISCLOSURE OF THE INVENTION

[0006] In view of the aforementioned problems in the prior art, thepresent invention has for its object to provide a method of adjustingthe lattice constant of a substrate and to provide an in-plane latticeconstant adjusted substrate.

[0007] In order to achieve the object mentioned above, there is providedin accordance with the present invention in a first form ofimplementation thereof a method of preparing an in-plane latticeconstant adjusted substrate, characterized in that it comprises thesteps of: growing a first epitaxial thin film made of a first materialon a substrate at a first preestablished temperature; and heat-treatingat a second preestablished temperature the substrate having the firstepitaxial thin film grown thereon.

[0008] In the method of preparing an in-plane lattice constant adjustedsubstrate in accordance with the present invention, the said firstpreestablished temperature is a temperature that causes the said firstmaterial to epitaxially grow on the said substrate.

[0009] Also, the said second preestablished temperature is a temperaturethat is higher than the said first preestablished temperature but lowerthan the lower of melting points of the said substrate and the saidfirst epitaxial thin film.

[0010] According to this method makeup, epitaxially growing a firstmaterial on a substrate at a first preestablished temperature causes afirst epitaxial thin film having distortions due to its mismatch inin-plane lattice constant with the substrate to epitaxially grow on thesubstrate, and heat-treating the epitaxial thin film and the substrateat a second preestablished temperature introduces dislocations into thesubstrate surface and relaxes the in-plane lattice constant of the firstepitaxial thin film to a value close to the lattice constant of bulkcrystal of the first material. The dislocations are anchored to theinterface between the substrate and the first epitaxial thin film, thetop surface of the epitaxial thin film is flattened to an atomic level,and they are left immobile when another material is epitaxially grown onthat surface.

[0011] In the present invention, the said substrate and the said firstepitaxial thin film are preferably made of oxides. It is also preferredthat the said substrate be made of SrTiO₃ crystal and said firstepitaxial thin film be made of BaTiO₃.

[0012] According to this method makeup, it is possible to adjust thein-plane lattice constant of a single crystal substrate of SrTiO₃ whichis of low cost and stout, to the lattice constant of BaTiO₃. Also in anapplication in which the in-plane lattice constant of BaTiO₃ isrequired, it can be used in place of a BaTiO₃ which is brittle and ofhigh cost. For example, it becomes possible to manufacture at a low costBaTiO₃ capacitors which are high in dielectric constant.

[0013] The present invention also provides in another form ofimplementation thereof a method of preparing an in-plane latticeconstant adjusted substrate, characterized in that it comprises thesteps of: forming on a single crystal substrate whose surface is flat onan atomic level, a first epitaxial thin film having a first preselectedfilm thickness and made of a first material that is different from amaterial of which the substrate is made, and then forming on the firstepitaxial thin film, a second epitaxial thin film having a secondpreselected film thickness and made of a second material that contains,at a predetermined ratio of components, a substance of said firstmaterial and another substance which is capable of forming a solidsolution; and thereafter heat-treating them at a second preestablishedtemperature that is higher than an epitaxial growth temperature of thesaid first and second epitaxial thin films but lower than the lowest ofmelting points of the said substrate, the said first epitaxial thin filmand the said second epitaxial thin film to introduce dislocations intoan interface between the said substrate and the said first epitaxialthin film and an interface between the said first and second epitaxialthin films, whereby a modification of the said substrate ensures havingan in-plane lattice constant of the said second epitaxial thin filmcontrollably determined by a ratio of the said first to second filmthickness and/or a said predetermined ratio of components and having thetop surface of the said second epitaxial thin film flattened to anatomic level.

[0014] Also, the said second epitaxial thin film may be formed to thesecond preselected film thickness on the said substrate without usingthe said first epitaxial thin film made of the first material and maythereafter be heat-treated at the second preestablished temperature.

[0015] According to this method makeup, on the substrate there isallowed to epitaxially grow a first epitaxial thin film havingdistortions due to its mismatch in in-plane lattice constant with thesubstrate, and on the first epitaxial thin film there is allowed to growepitaxially a second epitaxial thin film having distortions due to itsmismatch in in-plane lattice constant with the first epitaxial thinfilm, and then heat-treating them at a second preestablished temperatureintroduces dislocations into the substrate surface and into theinterface between the first and second epitaxial thin films and relaxesthe in-plane lattice constants of the first and second epitaxial thinfilms to values close to the lattice constant of the bulk crystal of thesecond material.

[0016] The dislocations are anchored to the interfaces between thesubstrate and the first epitaxial thin film and between the latter andthe second epitaxial thin film, the top surface of the second epitaxialthin film is flattened to an atomic level, and the dislocations are leftimmobile when another material is caused to grow epitaxially on thatsurface.

[0017] Suitably selecting the ratio of components of the other substancein the said second material allows a desired in-plane lattice constantdetermined by the selected ratio of components and hence a substratehaving such a desired in-plane lattice constant to be obtained.

[0018] Further, the said substrate and the said first and secondepitaxial thin films are preferably made of oxides. It is preferred thatthe said substrate be a SrTiO₃ crystalline substrate, the said firstepitaxial thin film be made of BaTiO₃ and the said second epitaxial thinfilm be made of Ba_(x)Sr_(1-x)TiO₃ where 0<x<1.

[0019] According to this method makeup, suitably selecting x allowsforming a substrate which agrees in in-plane lattice constant with athin film to be formed thereon. Thus, for example, such a substrate canbe used for forming a (Ba, Sr) CuO or like oxide superconductor thinfilm thereon. Then, since a substrate can be formed which by selecting xsuitably is made substantially identical in in-plane lattice constant toa superconductor layer to be formed thereon, it becomes possible toobtain an oxide high-temperature superconductor film that extremelyexcels in quality. It is also possible to adjust the in-plane latticeconstant of the second epitaxial thin film by adjusting the ratio infilm thickness of the first to second epitaxial thin film.

[0020] The present invention also provides an in-plane lattice constantadjusted substrate, characterized in that it comprises a crystallinesubstrate made of SrTiO₃ and having a thin film of BaTiO₃ formedthereon, wherein the BaTiO₃ thin film has its top surface flattened toan atomic level and is substantially equal in lattice constant to BaTiO₃bulk crystal. A substrate so made up may be used, in an application inwhich a BaTiO₃ substrate is required, to replace the same which isbrittle and of high cost.

[0021] The present invention also provides a in-plane lattice constantadjusted substrate, characterized in that it comprises a crystallinesubstrate made of SrTiO₃ and having a thin film of BaTiO₃ formed thereonand a thin film of Ba_(x)Sr_(1-x)TiO₃ (where 0<x<1) formed on the BaTiO₃thin film, wherein the Ba_(x)Sr_(1-x)TiO₃ thin film has its top surfaceflattened to an atomic level and has its lattice constant adjustable toa desired length between the lattice constants of SrTiO₃ and BaTiO₃ bulkcrystals by selecting x. A substrate so made up can be used in forming athin film thereon. Then, since a substrate can be formed that agrees inin-plane lattice constant to a thin film to be formed thereon, it ispossible to form a thin film that extremely excels in quality.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will better be understood from thefollowing detailed description and the drawings attached hereto showingcertain illustrative forms of implementation of the present invention.In this connection, it should be noted that such forms of implementationillustrated in the accompanying drawings hereof are intended in no wayto limit the present invention but to facilitate an explanation andunderstanding thereof. In the drawings:

[0023]FIG. 1 shows typical views illustrating the principles ofpreparing an in-plane lattice constant adjusted substrate according to afirst form of implementation of the present invention;

[0024]FIG. 2 shows typical views illustrating the principles ofpreparing an in-plane lattice constant adjusted substrate according to asecond form of implementation of the present invention;

[0025]FIG. 3 shows images by a scanning tunnel electron microscope of asubstrate surface, an epitaxial thin film surface before a heattreatment and the epitaxial thin film surface after the heat treatmentin the first form of implementation of the present invention;

[0026]FIG. 4 shows an image taken by an atomic force microscope (AFM) ofan in-plane lattice constant adjusted substrate surface according to thefirst form of implementation of the present invention;

[0027]FIG. 5 shows images of a specimen comprising a SrTiO₃ substratewith a BaTiO₃ thin film epitaxially grown thereon in the first form ofimplementation of the present invention, which is taken by atransmission electron diffraction microscope (TEM) in a directionperpendicular to the substrate surface, wherein FIG. 5(a) is an TEMimage where spots therein correspond to lattice points and FIG. 5(b) isa figure obtained when the image of FIG. 5(a) is processed so as tovisualize the continuity of lattice planes;

[0028]FIG. 6 shows images of a specimen comprising a SrTiO₃ substratehaving a BaTiO₃ thin film epitaxially grown on it and thereafterheat-treated in the first form of implementation of the presentinvention, which is taken by the transmission electron diffractionmicroscope (TEM) in a direction perpendicular to the substrate surface,wherein FIG. 6(a) is an TEM image where spots therein correspond tolattice points and FIG. 6(b) is a figure obtained when the image of FIG.6(a) is processed so as to visualize the continuity of lattice planes;

[0029]FIG. 7 is a chart illustrating a result of measurement by afour-axis X-ray diffraction apparatus of a distribution of latticeconstants in an in-plane lattice constant adjusted substrate accordingto the first form of implementation of the present invention;

[0030]FIG. 8 shows an image by the atomic force microscope (AFM) of thesurface of an in-plane lattice constant adjusted substrate according tothe second form of implementation of the present invention; and

[0031]FIG. 9 shows an image by the four-axis X-ray diffraction apparatusof a distribution of lattice constants in an in-plane lattice constantadjusted substrate according to the second form of implementation of thepresent invention.

BEST MODES FOR CARRYING OUT THE INVENTION

[0032] Hereinafter, the present invention will be described in detailwith reference to certain suitable forms of implementation thereofillustrated in the drawing figures.

[0033] At the outset, mention is made of a first form of implementationof the present invention.

[0034]FIG. 1 shows typical views illustrating the principles ofpreparing an in-plane lattice constant adjusted substrate according to afirst form of implementation of the present invention wherein asubstrate 1 has a first epitaxial thin film 2 of a first material formedthereon. FIG. 1(a) shows a state in crystal lattice of the substrate 1and the first epitaxial thin film 2 typically in a cross section takenperpendicular to a surface 3 of the substrate. The crystal lattices inthe substrate 1 and those in the first epitaxial thin film 2 aretypically represented by squares and rectangles, respectively, as shown.FIG. 1(b) shows a state of the crystal lattice after the heat-treatmentof the substrate 1 formed with the first epitaxial thin film 2 on it,which are shown typically in a cross section taken perpendicular to thesubstrate surface 3. The crystal lattices in the substrate 1 and thosein the first epitaxial thin film 2 after the heat treatment are againtypically represented by squares and rectangles, respectively, as shown.

[0035] The method of preparing an in-plane crystal lattice adjustingsubstrate comprises a first step of supplying the substrate 1 at a firstpreestablished temperature with a first material over it to grow a firstepitaxial thin film 2 composed of the first material on the substrate 1.The first preestablished temperature may be any low or high temperatureif it allows the epitaxial growth of the first epitaxial thin film 2.Here, any epitaxial growth process, such as MOCVD, CVD or laserablation, may be adopted in epitaxially growing the first material onthe substrate 1.

[0036] As shown in FIG. 1(a), the first epitaxial thin film 2 is formedon the substrate so that the lattice planes in the first epitaxial thinfilm 2 are substantially continuous with those in the substrate 1 andthat the in-plane lattice constant a₁ in the first epitaxial thin film 2is substantially equal to the in-plane lattice constant as in thesubstrate 1. Also the lattice constant of the first epitaxial thin film2 in a direction perpendicular to the substrate surface 3 is differentfrom the lattice constant of the first material in its bulk state.Therefore the first epitaxial thin film 2 is grown on the substrate 1 ina state that it has distortions due to its mismatch in in-plane latticeconstant with the substrate 1.

[0037] Then, the substrate 1 on which the first epitaxial thin film 2has been grown is heat-treated at a second preestablished temperature,which is a temperature higher than the first preestablished temperature,but lower than the lower of the melting points of the substrate 1 andthe first epitaxial thin film 2.

[0038] With this heat treatment, as shown in FIG. 1(b), a dislocation 4is introduced into the substrate surface 3 while the distortions in thefirst epitaxial thin film 2 is relieved with the result that thein-plane lattice constant a₁ in the first epitaxial thin film 2 becomessubstantially equal to the lattice constant of the first material in itsbulk state. Further, its lattice constant in a direction perpendicularto the substrate surface 3 also relaxes and becomes substantially equalto the lattice constant in its bulk state. The dislocations 4 areanchored to the substrate surface 3 while the first epitaxial thin film2 has its top surface 5 flattened to an atomic level, thereby permittinganother material to grow epitaxially thereon while leaving thedislocations 4 anchored immobile.

[0039] Mention is next made of a second form of implementation of thepresent invention.

[0040]FIG. 2 shows typical views illustrating the principles ofpreparing an in-plane lattice constant adjusted substrate according to asecond form of implementation of the present invention, wherein asubstrate 1 has a first epitaxial thin film 2 of a first material formedthereon by a preselected film thickness, which in turn has a secondepitaxial thin film 6 of a second material formed thereon by apredetermined thickness. FIG. 2(a) shows a state in crystal lattice ofthe substrate 1, the first epitaxial thin film 2 and the secondepitaxial thin film 6 typically in a cross section taken perpendicularto a surface 3 of the substrate 1. The crystal lattices of the substrate1 and the crystal lattices of the first and second epitaxial thin films2 and 6 are typically represented by squares and rectangles,respectively, as shown.

[0041]FIG. 2(b) shows a state in crystal lattice of the substrate 1 andthe first and second epitaxial thin films 2 and 6 which are formed asmentioned above and then are heat-treated at a second preestablishedtemperature. The state is shown typically in a cross section takenperpendicular to the substrate surface 3. The crystal lattices of thesubstrate 1 and those of the first and second epitaxial thin films 2 and6 are again typically represented by squares and rectangles,respectively, as shown.

[0042] The method of a preparing an in-plane lattice constant adjustedsubstrate of the present invention in this form of implementationcomprises a first step of supplying a substrate 1 at a firstpreestablished temperature with a first material over it to grow a firstepitaxial thin film 2 of a first predetermined film thickness on thesubstrate 1 and subsequently supplying a second material to grow asecond epitaxial thin film 6 of a second predetermined film thicknessthereon. Here, the first predetermined film thickness is madesufficiently thinner than the second predetermined film thickness. Thesecond material should contain a substance of the first material andanother substance that is capable of forming a solid solution togetherwith that substance, at a preselected ratio of components. The firstpreestablished temperature may be any low or high temperature if itallows the epitaxial growth of the thin film. Here, any epitaxial growthprocess, such as MOCVD, CVD or laser ablation, may be adopted inepitaxially growing the first and second materials on the substrate 1.

[0043] As shown in FIG. 2(a), the first and second epitaxial thin filmsare formed on the substrate so that the lattice planes in the first andsecond epitaxial thin films 2 and 6 are substantially continuousmutually and with those in the substrate 1 and that the in-plane latticeconstants a₁ and a₂ in the first and the second epitaxial thin films 2and 6 are substantially equal to the in-plane lattice constant a_(a) inthe substrate 1. Therefore, the first and second epitaxial thin films 2and 6 are epitaxially grown on the substrate 1 in a state that they havedistortions due to their mismatch in in-plane lattice constant.

[0044] Then, the substrate 1 on which the epitaxial thin films 2 and 6have been grown is heat-treated at a second preestablished temperaturewhich is a temperature higher than the first preestablished temperature,but lower than the lowest of the melting points of the substrate 1 andthe first and second epitaxial thin films 2 and 6. With this heattreatment, as shown in FIG. 2(b), dislocations 4 are introduced intoboth the substrate surface 3 and the interface 7 between the first andsecond epitaxial thin films 2 and 6 or the substrate surface 3 alone torelax the in-plane lattice constants in the first and second epitaxialthin films 2 and 6. Further, with the first predetermined film thicknessmade sufficiently thinner than the second predetermined film thickness,the in-plane lattice constants of the first and second epitaxial thinfilms 2 and 6 relax to a value close to the lattice constant of thesecond material in its bulk crystal state. The in-plane lattice constanta₂ changes according to the component ratio of the second material,namely the ratio in amount of the substance of the first material to theother substance forming the solid solution together therewith. Theirlattice constants in a direction perpendicular to the substrate surface3 also relax. The dislocations 4 are anchored to both the substratesurface 3 and the interface 7 or to the substrate surface 3 alone whilethe second epitaxial thin film 6 has its top surface 8 flattened to anatomic level, thereby permitting another material to grow epitaxiallythereon while leaving the dislocations anchored immobile.

[0045] The present invention thus enables the in-plane lattice constantof a substrate to be adjusted to a desired value, thereby permitting adevice preparation process using an epitaxial thin film to be furnishedwith a substrate having an optimum in-plate lattice constant.

[0046] Mention is next made of a specific example of the first form ofimplementation of the present invention.

[0047] A specific example is here shown in which a substrate of SrTiO₃crystal is adjusted to have a in-plane lattice constant of BaTiO₃. As aspecimen the SrTiO₃ crystal substrate was formed thereon at an epitaxialgrowth temperature of 650° C. with an epitaxial thin film of BaTiO₃ asthe first epitaxial thin film to a film thickness of 120 angstroms bylaser ablation in a vacuum chamber, and then in the same vacuum chamberwas heat-treated to a temperature of about 1350° C. for a period ofabout 1 hour by laser heating.

[0048]FIG. 3 shows images by a scanning tunnel electron microscope of asubstrate surface, an epitaxial thin film surface before the heattreatment and an epitaxial thin film surface after the heat treatment.The BaTiO₃ epitaxial thin film grown on the SrTiO₃ crystal substratewhose surface is flat on an atomic level as shown in FIG. 3(a) is seento have a top surface that is keenly irregular or uneven as shown inFIG. 3(b). With the heat treatment applied to the substrate, a film topsurface that is flat or even on an atomic level as shown in FIG. 3(c)has obtained. Each of vertical stripes in FIGS. 3(a) and 3(c) representsan atomic surface step which corresponds to mono-molecular layer, and aregion between the adjacent vertical stripes represents an identicalatomic surface. FIG. 4 shows an image taken by an atomic forcemicroscope (AFM) of the surface of the specimen after the heattreatment. Each of vertical stripes seen in the figure represents atomicsurface step which corresponds to mono-molecular layer, and a regionbetween the adjacent vertical stripes represents an identical atomicsurface. From FIGS. 3 and 4, it is seen that the top surface of theBaTiO₃ epitaxial thin film is flat and even on an atomic level.

[0049]FIG. 5 shows images of a specimen comprising a SrTiO₃ substratewith a BaTiO₃ thin film epitaxially grown thereon, which is taken by atransmission electron diffraction microscope (TEM) in a directionperpendicular to the substrate surface, wherein FIG. 5(a) is an TEMimage where spots therein correspond to lattice points and FIG. 5(b) isa figure obtained when the image of FIG. 5(a) is processed so as tovisualize the continuity of lattice planes. From FIG. 5 it is seen thatthe substrate and the epitaxial thin film are almost continuous witheach other in lattice planes and that the epitaxial thin film has alarge number of discontinuities of lattice planes, namely dislocationstherein.

[0050]FIG. 6 shows images of a specimen comprising a SrTiO₃ substratehaving a BaTiO₃ thin film epitaxially grown on it and thereafterheat-treated, which is taken by the transmission electron diffractionmicroscope (TEM) in a direction perpendicular to the substrate surface,wherein FIG. 6(a) is an TEM image where spots therein correspond tolattice points and FIG. 6(b) is a figure obtained when the image of FIG.6(a) is processed so as to visualize the continuity of lattice planes.In FIG. 6(a) it is seen that lattice points lie more orderly than inFIG. 5(a). From FIG. 6(b) it is seen that dislocations exist only on thesubstrate surface, and not at all on epitaxial thin film. From theseresults it is seen that according to the method of the present inventionthe dislocations are anchored to the substrate surface and the topsurface of the first epitaxial thin film is flattened to an atomiclevel.

[0051]FIG. 7 is a chart illustrating a result of measurement by afour-axis X-ray diffraction apparatus of a distribution of latticeconstants in the specimen mentioned above. In the chart, the abscissaand ordinate axes are taken in the (300) and (003) directions of areciprocal lattice space, respectively. In the chart, the point Aindicates the diffraction point of the BaTiO₃ epitaxial thin film whereits diffraction intensity is the maximum, and the point B indicates thediffraction point of the SrTiO₃ crystal substrate where its diffractionintensity is the maximum. From the coordinate of point A it is seen thatthe in-plane lattice constant a of the BaTiO₃ epitaxial thin film is3.990 angstroms, which is approximately equal to the lattice constant ofBaTiO₃ bulk crystal (a=4.000 angstroms). It is seen that according tothe method of the present invention, the in-plane lattice constant ofthe first epitaxial thin film is relaxed to the lattice constant of itsbulk crystal.

[0052] Mention is next made of a specific example of the second form ofimplementation of the present invention. Here, a specific example isshown in which a substrate of SrTiO₃ crystal is adjusted to have adesired in-plane lattice constant. As a specimen the SrTiO₃ crystalsubstrate was formed thereon at an epitaxial growth temperature of 650°C. with an epitaxial thin film of BaTiO₃ as a first epitaxial thin filmto a film thickness of 120 angstroms and then formed thereon at anepitaxial growth temperature of 650° C. with an epitaxial thin film ofBa_(0.5)Sr_(0.5)TiO₃ as a second epitaxial thin film to a film thicknessof 1800 angstroms, each by laser ablation in a vacuum chamber, and thenin the same vacuum chamber was heat-treated to a temperature of about1350° C. for a period of about 1 hour by laser heating.

[0053]FIG. 8 shows an image taken by the atomic force microscope (AFM)of the surface of the specimen after the heat treatment. In the Figure,vertical stripes represent atomic surface steps each of whichcorresponds to mono-molecular layer, and a region between the adjacentvertical stripes represents an identical atomic surface. From the Figureit is seen that the surface of Ba_(0.5)Sr_(0.5)TiO₃ epitaxial thin filmis flat on an atomic level. Thus, according to the method of the presentinvention, the dislocations are anchored to the substrate surface, andthe surface of the second epitaxial thin film is flattened to an atomiclevel.

[0054]FIG. 9 is a figure illustrating a result of measurement by afour-axis X-ray diffraction apparatus of a distribution of latticeconstants in the specimen mentioned above. In the figure, the abscissaand ordinate axes are taken in the (300) and (003) directions of areciprocal lattice space, respectively. In the figure, the point Cindicates the diffraction point of the Ba_(0.5)Sr_(0.5)TiO₃ epitaxialthin film as the second epitaxial thin film where its diffractionintensity is the maximum, and the point A indicates the diffractionpoint of the BaTiO₃ epitaxial thin film as the first epitaxial thin filmwhere its diffraction intensity is the maximum. From the coordinate ofpoint C it is seen that the in-plane lattice constant a of theBa_(0.5)Sr_(0.5)TiO₃ epitaxial thin film is 3.952 angstroms, which is avalue as a lattice constant intermediate between the lattice constant ofSrTiO₃ bulk crystal of the substrate (a=3.905 angstroms) and the latticeconstant of BaTiO₃ bulk crystal (a=4.000 angstroms). From the coordinateof point A it is seen that the in-plane lattice constant a of the BaTiO₃epitaxial thin film as the first epitaxial thin film is 3.955 angstroms,which is a value as a lattice constant approximately equal to thein-plane lattice constant of Ba_(0.5)Sr_(0.5)TiO₃ mentioned above. Thefact that the film thickness of Ba_(0.5)Sr_(0.5)TiO₃ being 1800angstroms is much thicker than the film thickness of BaTiO₃ being 120angstroms allows the in-plane lattice constant of the BaTiO₃ epitaxialthin film as the first epitaxial thin film to take a value close to thein-plane lattice constant of Ba_(0.5)Sr_(0.5)TiO₃.

[0055] Changing the ratio in thickness of the first to the secondepitaxial growth films changes the in-plate lattice constants of thefirst and second epitaxial thin films. It is also possible to adjust thein-plane lattice constants by way of only the film thickness of thesecond epitaxial thin film.

[0056] While in this specific example the ratio x of components is made0.5, it will be apparent that suitably changing the ratio x allowsrealizing a desired in-plane lattice constant intermediate between thelattice of substrate SrTiO₃ (a=3.952 angstroms) and the lattice constantof bulk BaTiO₃ (a=4.000). According to the method of the presentinvention it is thus seen that suitably selecting the ratio of componentx allows adjusting the in-plane lattice constant of a second epitaxialthin film to have a desired value.

[0057] While in the foregoing description the heat-treatment temperatureis shown to be lower than the melting points of materials used, somematerials have constituent atoms diffusing in their solid state. Withsuch materials, it is desirable that the heat treatment be effected at atemperature lower than their solid-state diffusion startingtemperatures, namely their sintering temperatures.

[0058] Also, while in the foregoing specific examples, an example istaken of oxides having a perovskite-type crystallographic structure, itshould be apparent that the oxides may be those having a differentcrystallographic structure, e. g., of a hexagonal system. It should alsobe apparent that the materials to which the present invention isapplicable are not limited to oxides and may be any other materials.

INDUSTRIAL APPLICABILITY

[0059] As will be appreciated from the foregoing description, thepresent invention makes it possible to adjust the in-plane latticeconstant of a substrate to have a desired value. Accordingly, the use ofan in-plane lattice constant adjusted substrate of the present inventionfor a device utilizing an epitaxial thin film allows the device to beprepared having an extremely high quality. The present invention isextremely useful when used as a substrate, e. g., for high temperatureoxide superconducting device.

What is claimed is:
 1. A method of preparing an in-plane latticeconstant adjusted substrate, characterized in that it comprises thesteps of: forming at a first preestablished temperature on a singlecrystal substrate whose surface is flat on an atomic level, a firstepitaxial thin film made of a first material that is different from amaterial of which the substrate is made; and heat-treating at a secondpreestablished temperature the substrate having the first epitaxial thinfilm formed thereon, wherein said first preestablished temperature is atemperature that causes said first epitaxial thin film to epitaxiallygrow on said substrate; and said second preestablished temperature is atemperature that is higher than said first preestablished temperaturebut lower than the lower of melting points of said substrate and saidfirst epitaxial thin film, whereby the heat treatment at the secondpreestablished temperature gives rises to a modification of saidsubstrate such that dislocations are introduced into an interfacebetween the substrate and the first epitaxial thin film whereby thein-plane lattice constant of the first epitaxial thin film is altered tohave a value that is close to a bulk lattice constant of said firstmaterial, and such that the top surface of said first epitaxial thinfilm is flattened to an atomic level.
 2. (Deleted)
 3. (Deleted)
 4. Amethod of preparing an in-plane lattice constant adjusted substrate asset forth in claim 1, characterized in that said substrate and saidfirst epitaxial thin film are made of oxides.
 5. A method of preparingan in-plane lattice constant adjusted substrate as set forth in claim 1,characterized in that said substrate is a SrTiO₃ crystalline substrateand said first epitaxial thin film is made of BaTiO₃.
 6. A method ofpreparing an in-plane lattice constant adjusted substrate, characterizedin that it comprises the steps of: forming on a single crystal substratewhose surface is flat on an atomic level, a first epitaxial thin filmhaving a first preselected film thickness and made of a first materialthat is different from a material of which the substrate is made, andthen forming on the first epitaxial thin film, a second epitaxial thinfilm having a second preselected film thickness and made of a secondmaterial that contains, at a predetermined ratio of components, asubstance of said first material and another substance which is capableof forming a solid solution; and thereafter heat-treating them at asecond preestablished temperature that is higher than an epitaxialgrowth temperature of said first and second epitaxial thin films butlower than the lowest of melting points of said substrate, said firstepitaxial thin film and said second epitaxial thin film to introducedislocations into an interface between said substrate and said firstepitaxial thin film and an interface between said first and secondepitaxial thin films, whereby a modification of said substrate ensureshaving an. in-plane lattice constant of said second epitaxial thin filmcontrollably determined by a ratio of said first to second filmthickness and/or a said predetermined ratio of components and having thetop surface of said second epitaxial thin film flattened to an atomiclevel.
 7. A method of preparing an in-plane lattice constant adjustedsubstrate as set forth in claim 6, characterized in that said secondepitaxial thin film is formed having an in-plane lattice constantcontrollably determined by only a ratio of components thereof withoutforming said first epitaxial thin film made of the first material. 8.(Deleted)
 9. (Deleted)
 10. (Deleted)
 11. A method of preparing anin-plane lattice constant adjusted substrate as set forth in claim 6,characterized in that said substrate and said first and second epitaxialthin films are made of oxides.
 12. A method of preparing an in-planelattice constant adjusted substrate as set forth in claim 6,characterized in that said substrate is a SrTiO₃ crystalline substrate,said first epitaxial thin film is made of BaTiO₃ and said secondepitaxial thin film is made of Ba_(x)Sr_(1-x)TiO₃ where 0<x<1.
 13. Anin-plane lattice constant adjusted substrate, characterized in that itcomprises a SrTiO₃ crystalline substrate and having a thin film ofBaTiO₃ formed thereon, wherein the BaTiO₃ thin film has its top surfaceflattened to an atomic level and is substantially equal in latticeconstant to BaTiO₃ bulk crystal.
 14. An in-plane lattice constantadjusted substrate, characterized in that it comprises a SrTiO₃crystalline substrate and having a thin film of BaTiO₃ formed thereonand a thin film of Ba_(x)Sr_(1-x)TiO₃ (where 0<x<1) formed on the BaTiO₃thin film, wherein the Ba_(x)Sr_(1-x)TiO₃ thin film has its top surfaceflattened to an atomic level and has its in-plate lattice constantadjustable to a desired length between the lattice constants of SrTiO₃and BaTiO₃ bulk crystals by selecting x.